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How is a truss, which undergoes rigid body translation for an arbitrary load, classified as?

How is a truss, which undergoes rigid body translation for an arbitrary load, classified as? Correct Answer Structurally unstable structure

Explanation

The stability or instability of a truss depends upon the loading conditions it is facing. It isn’t necessary that a truss not containing a triangular element is unstable. It can be stable or unstable again it is decided by the loading pattern. 

When the degree of static indeterminacy of a structure is equal to zero then that structure is known as determinate structure, as all the unknown forces can be calculated using the equilibrium equations only.

Steps to check the stability of a truss:

First, calculate the degree of static indeterminacy. (Dsi)

If Dsi < 0, then the structure is unstable – This is known as statically unstable structure.

Dsi > 0 , then structure is unstable if

  • All the reactions are parallel.
  • All the reactions are concurrent.

When a truss undergoes rigid body translation for an arbitrary load, that is known as structurally unstable structure.

Important Points

a) Below are the figures for the references:

[ alt="F2 N.M Madhu 23.03.20 D5 " src="//storage.googleapis.com/tb-img/production/20/03/F2_N.M_Madhu_23.03.20_D5_.png" style="width: 224px; height: 161px;">

For this particular loading pattern, the non-triangular truss structure is stable.

If a horizontal load is introduced in the above truss arrangement, it will become unstable.

b) A truss structure is externally unstable if all of its reactions are parallel or concurrent. This is because, if the reactions are parallel then it won’t generate reaction for a transverse force. Also, if it is concurrent, then also no reactions would be generated to handle the non-concurrent point.

[ alt="F2 N.M Madhu 23.03.20 D6 " src="//storage.googleapis.com/tb-img/production/20/03/F2_N.M_Madhu_23.03.20_D6_.png" style="width: 223px; height: 185px;">

There is no reaction to balance H force, hence the above truss is unstable.

[ alt="F2 N.M Madhu 23.03.20 D7 " src="//storage.googleapis.com/tb-img/production/20/03/F2_N.M_Madhu_23.03.20_D7_.png" style="width: 319px; height: 177px;">

If a moment about A is taken as zero then, all reaction moments would be zero and hence the above truss is unstable.

c) A truss is internally unstable if all the forces acting inside are concurrent to each other and hence non-concurrent forces would not be balanced by any of them. Below is the figure for reference:

[ alt="F2 N.M Madhu 23.03.20 D8 " src="//storage.googleapis.com/tb-img/production/20/03/F2_N.M_Madhu_23.03.20_D8_.png" style="width: 200px; height: 163px;">

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